A358974 a(n) is the least prime p such that q-p = n*(r-q) where p,q,r are consecutive primes.

3, 7, 23, 6397, 139, 509, 84871, 1933, 1259, 43331, 1129, 4523, 933073, 2971, 6917, 1568771, 9973, 32261, 4131109, 25261, 78737, 12809359, 91033, 28229, 13626257, 35677, 117443, 37305713, 399793, 102701, 217795247, 288583, 296843, 240485257, 173359, 1025957, 213158279, 1053103, 370949, 1163010181

Offset: 1

Author

Robert Israel and Juri-Stepan Gerasimov, Dec 07 2022

Keywords

• nonn

Comments

a(n) = prime(k) for the first k such that A001223(k) = n*A001223(k+1).

Examples

			a(3) = 23 because 23, 29, 31 are consecutive primes with 29-23 = 3*(31-29) and 23 is the first prime that works.
		

Crossrefs

Cf. A001223, A179256, A181994.

Programs

Maple

V:= Vector(45): count:= 0:
q:= 2: r:= 3:
while count < 45 do
  p:= q; q:= r; r:= nextprime(r);
  v:= (q-p)/(r-q);
  if v::integer and v <= 45 and V[v] = 0 then
    count:= count+1; V[v]:= p;
  fi
od:
convert(V,list);

Python

from sympy import nextprime
from itertools import count, islice
def agen():
    p, q, r, n, adict = 2, 3, 5, 1, dict()
    while True:
        v, rem = divmod(q-p, r-q)
        if rem == 0 and v not in adict: adict[v] = p
        while n in adict: yield adict[n]; n += 1
        p, q, r = q, r, nextprime(r)
print(list(islice(agen(), 21))) # Michael S. Branicky, Dec 07 2022